Generously coat six 6-ounce ramekins with softened butter. Chill in the freezer for about 10 minutes, and brush with a second coat of butter. Pour 3 tablespoons caramel sauce into the bottom of each ramekin and transfer to the freezer for 1 hour.

Whisk the cake flour, cocoa, baking soda, sugar, and salt together in a large bowl and set aside. Stir the coffee, oil, vanilla, and vinegar together and whisk into the flour mixture just until smooth.

Fill each ramekin with 1/3 cup of batter. Bake at 400 degrees F until the cake is set and a toothpick inserted in the center comes out clean, and the caramel has bubbled up the sides, about 20 minutes.